Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201912 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
12 April
Shift
Evening Shift
Subject
Physics
Chapter
Motion in Two Dimensions

JEE Main 2019 · 12 April · Evening Shift · Physics · Motion in Two Dimensions

Two particles are projected from the same point with the same speed...

Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h1{h}_{1} and h2.{h}_{2} . Which of the following is correct?

Options

  1. AR2=h1h2{R}^{2} = {h}_{1}{h}_{2}
  2. BR2=4h1h2{R}^{2} = 4{h}_{1}{h}_{2}
  3. CR2=2h1h2{R}^{2} = 2{h}_{1}{h}_{2}
  4. DR2=16h1h2{R}^{2} = 16{h}_{1}{h}_{2}

Correct answer

D. R2=16h1h2{R}^{2} = 16{h}_{1}{h}_{2}

Step-by-step solution

We get same range for angle of projections θ\theta and 90−θ90 - \theta .
h=u2sin⁡2θ2gh = \dfrac{{u}^{2}\sin^{2}\theta}{2g}
⇒h1=u2sin⁡2θ2g,h2=u2cos⁡2θ2g⇒ {h}_{1} = \dfrac{{u}^{2}\sin^{2}\theta}{2g}, {h}_{2} = \dfrac{{u}^{2}\cos^{2}\theta}{2g}
h1h2=u4sin⁡2θcos2θ4g2=4u4sin⁡2θcos⁡2θ16g2{h}_{1}{h}_{2} = \dfrac{{u}^{4}\sin^{2}{\theta cos}^{2}\theta}{4{g}^{2}} = \dfrac{{4u}^{4}\sin^{2}\theta\cos^{2}\theta}{16{g}^{2}}
=(u2sin⁡2θg)2116=R216= {\left(\dfrac{{u}^{2}\sin 2\theta}{g}\right)}^{2}\dfrac{1}{16} = \dfrac{{R}^{2}}{16}
∴R2=16h1h2∴ {R}^{2} = 16{h}_{1}{h}_{2}
Practice Motion in Two Dimensions on Quantrex Academy →

More from Motion in Two Dimensions

A particle is thrown with a speed v from a point O at an angle θ with the horizontal… JEE Advanced 2026A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is… JEE Main 2026Two identical bodies, projected with the same speed at two different angles cover the… JEE Main 2026If x and y coordinates of a projectile as a function of time (t) are given as 24t and… JEE Main 2026A gun mounted on the ground fires bullets in all directions with same speed. The farthest… JEE Main 2026Two projectiles are projected with the same initial velocities at the 15^∘ and 30^∘ with… JEE Main 2026A boy throws a ball into air at 45^ ∘ from the horizontal to land it on a roof of a… JEE Main 2026An object is projected with kinetic energy K from a point A at an angle 60^ ∘ with the… JEE Main 2026 Full Motion in Two Dimensions list All JEE Main PYQs